What the heck is a node, anyway????? September 26, 2005

So far we have discussed A little music physics Tones Waves Frequencies Wavelengths Standing Waves Some musical Instruments

BUT …. We really haven’t much discussed

We HAVE mentioned that Sound travels through the air. Sound is a “pressure” wave. We discussed pressure (force/unit area) Normal Atmospheric Pressure (14 psi or 101,300 Pa [N/m 2 ] or 1 bar) Sound travels at about 1100 ft/sec or 344 m/sec. A loud sound represents a pressure of only 1/10,000 th of an atmosphere.

Speed of sound is affected by Temperature Humidity (Very Slight) Density of the gas (air)

Temperature (Check my Arithmetic, please) The speed of sound increases by 1.1 ft/sec for every Fahrenheit degree of increased temperature. For a tube open at both ends, the fundamental frequency was shown to be: v/2L. A 10 0 change will produce a corresponding frequency change of 11/1100 ~.001. For f=440, this is about ½ Hz. A bigger temperature change would be noticed by a trained musician. Larger temperature excursions are possible.

Gas We model a gas as a collection of spheres that are contained (usually) in a volume and that bump into each other from time to time. A pressure wave increases (or decreases) the density of these spheres.

An Impulse Pressure Wave

Moving along ~v

Process Repeats Itself …..

A Sound Wave is Born Fork is compressing the gas Fork is expanding the gas etc. SOUND

Oh where, oh where has my sound wave gone … Here? To be continued.

It eventually gets someplace

Down to the detail: We define the “quantity of motion” as the product of the mass and the velocity. momentum=mv momentum is conserved it remains constant

Collisions If energy is conserved, the first ball will stop and the second ball will move out with the velocity of the first. TOTAL momentum is therefore conserved for a SYSTEM of particles. momentum

A ball of air Pressure caused by the collisions with the wall of the enclosure. Motion of the molecules is RANDOM. Average velocity of the gas molecules is ZERO.

Pressure Wave Higher pressure region, higher density, Average velocity to the right. Lower pressure region, lower density, Average velocity also to the right.

A Wall

Oh, Oh, another wall!!! Average velocity at wall is zero Wave is reflected Wall is a velocity node but a Pressure Anti-node due to the wave itself. Lots of collisions!

Open End REFLECTION

The standing wave

Both Open and Closed Ends of Tubes Produce a Reflection

Lips

Nodes, etc. The entrance to the pipe is sealed from the atmosphere by the player's lips, and the pressure can vary maximally as the lips open and close: indeed, it is the large variation of pressure in the mouthpiece that (usually) forces the lips to vibrate at a resonance of the bore. So at this end we have a pressure antinode. Most of the time, the lips are closed so the lips represent a velocity node.